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Influence diagnostics on the coefficient of variation of elliptically contoured distributions

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  • Marco Riquelme
  • V�ctor Leiva
  • Manuel Galea
  • Antonio Sanhueza

Abstract

In this article, we study the behavior of the coefficient of variation (CV) of a random variable that follows a symmetric distribution in the real line. Specifically, we estimate this coefficient using the maximum-likelihood (ML) method. In addition, we provide asymptotic inference for this parameter, which allows us to contrast hypothesis and construct confidence intervals. Furthermore, we produce influence diagnostics to evaluate the sensitivity of the ML estimate of this coefficient when atypical data are present. Moreover, we illustrate the obtained results by using financial real data. Finally, we carry out a simulation study to detect the potential influence of atypical observations on the ML estimator of the CV of a symmetric distribution. The illustration and simulation demonstrate the robustness of the ML estimation of this coefficient.

Suggested Citation

  • Marco Riquelme & V�ctor Leiva & Manuel Galea & Antonio Sanhueza, 2011. "Influence diagnostics on the coefficient of variation of elliptically contoured distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 513-532, November.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:3:p:513-532
    DOI: 10.1080/02664760903521427
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    Cited by:

    1. Helio M. de Oliveira & Raydonal Ospina & Carlos Martin-Barreiro & Víctor Leiva & Christophe Chesneau, 2023. "On the Use of Variability Measures to Analyze Source Coding Data Based on the Shannon Entropy," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    2. Danilo Leal & Rodrigo Jiménez & Marco Riquelme & Víctor Leiva, 2023. "Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    3. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    4. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    5. Víctor Leiva & Shuangzhe Liu & Lei Shi & Francisco José A. Cysneiros, 2016. "Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 627-642, March.

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